Question

If f(x)=3-2xand g(x)= 1/x+5, what is the value of f/g (8)?

Answer 1

Answer:

$-\frac{104}{41}$

Step-by-step explanation:

$\frac{f(x)}{g(x)}=\frac{3-2x}{\frac{1}{x} +5}$

To make this easier to deal with, we can plug in 8 first:

• $\frac{f(8)}{g(8)}=\frac{3-2(8)}{\frac{1}{(8)}+5 }$
• Then we can simplify the terms to get $\frac{3-16}{\frac{1}{8} +5}=\frac{-13}{\frac{1}{8} +5}$
• The denominator of this fraction needs to have its own common denominator. To do so, we can multiply the 5 by $\frac{8}{8}$ to give us: $\frac{1}{8}+\frac{40}{8}$
• We can then simplify this to $\frac{41}{8}$
• Now putting this back into our original fraction we have: $\frac{-13}{\frac{41}{8} }$
• This is also equivalent to $\frac{(\frac{-13}{1} )}{(\frac{41}{8} )}$ which means we need to take the whole denominator of the fraction and flip it and multiply it by the numerator to get: $\frac{-13}{1}*\frac{8}{41}$
• This then simplifies to $\frac{-104}{41}$